Resequencing Calculus: Rationale An Early Multivariate Approach - - PowerPoint PPT Presentation

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Resequencing Calculus: Rationale An Early Multivariate Approach - - PowerPoint PPT Presentation

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Resequencing Calculus: Dwyer and Gruenwald Definition Resequencing Calculus: Rationale An Early Multivariate Approach Text Piloting Challenges David Dwyer and Mark Gruenwald Solutions University of Evansville Further Information January

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Resequencing Calculus: Dwyer and Gruenwald Definition Rationale Text Piloting Challenges Solutions Further Information

Resequencing Calculus:

An Early Multivariate Approach David Dwyer and Mark Gruenwald University of Evansville January 4, 2012

Supported by NSF Grant 0836676

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Resequencing Calculus: Dwyer and Gruenwald Definition Rationale Text Piloting Challenges Solutions Further Information

What is Early Multivariate Calculus?

A reformulation of the standard 3-semester calculus sequence in which Vectors, matrices, functions of several variables, double (but not triple) integrals are introduced in Calculus II. Infinite series is moved to Calculus III. Other minor changes are made to ensure balancing

  • f material across semesters.
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Resequencing Calculus: Dwyer and Gruenwald Definition Rationale Text Piloting Challenges Solutions Further Information

Rationale

Calculus II is a better jumping off point for some students in Biology, Chemistry, and Economics. Natural progression of difficulty through the sequence Prerequisites lowered to Calculus II for calculus-based probability, linear algebra, and differential equations. Facilitates complete treatment of vector calculus in Calculus III through Stokes’ Theorem and the Divergence Theorem.

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Resequencing Calculus: Dwyer and Gruenwald Definition Rationale Text Piloting Challenges Solutions Further Information

Calculus—An Early Multivariate Approach

Coverage of resequenced Calculus I and II (11 chapters) Extensive (700 pages, 1000 graphics, 2000 exercises) Discipline-specific projects

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Resequencing Calculus: Dwyer and Gruenwald Definition Rationale Text Piloting Challenges Solutions Further Information

Calculus—An Early Multivariate Approach

Coverage of resequenced Calculus I and II (11 chapters) Extensive (700 pages, 1000 graphics, 2000 exercises) Discipline-specific projects

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Resequencing Calculus: Dwyer and Gruenwald Definition Rationale Text Piloting Challenges Solutions Further Information

Piloting at Evansville

Entire sequence taught at UE by multiple faculty members New text used for Calculus I and II Parts of Stewart’s Early Transcendentals used for Calculus III Assessment supports viability of sequence

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Resequencing Calculus: Dwyer and Gruenwald Definition Rationale Text Piloting Challenges Solutions Further Information

Challenges

Using parts of an existing text for Calculus III Placement of students with dual, transfer, or AP-BC credit Systemic entrenchment of existing system Translating success at Evansville into workable model at other institutions

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Resequencing Calculus: Dwyer and Gruenwald Definition Rationale Text Piloting Challenges Solutions Further Information

Solutions

Expand text to include Calculus III Pilot sequence at other institutions Develop online multivariate modules to assist with placement of AP-BC and transfer students Develop evidence to support institutional change Work with MAA, AMATYC, and the AP to effect change

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Resequencing Calculus: Dwyer and Gruenwald Definition Rationale Text Piloting Challenges Solutions Further Information

Further Information

Mark Gruenwald mg3@evansville.edu David Dwyer dd4@evansville.edu Website resequencingcalculus.com

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Resequencing Calculus: Dwyer and Gruenwald Table of Contents

Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16

Revised Sequence

Chapter 1 - Functions

1.1 Functions and Their Graphs 1.2 Algebra of Functions 1.3 Library of Functions 1.4 Implicit Functions and Conic Sections 1.5 Polar Functions 1.6 Parametric Functions

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Resequencing Calculus: Dwyer and Gruenwald Table of Contents

Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16

Revised Sequence

Chapter 2 - Limits

2.1 Limits in Calculus 2.2 Limits: Numerical and Graphical Approaches 2.3 Calculating Limits Using Limit Laws 2.4 Limits at Infinity and Horizontal Asymptotes 2.5 Continuity and the Intermediate Value Theorem 2.6 The Precise Definition of a Limit

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Resequencing Calculus: Dwyer and Gruenwald Table of Contents

Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16

Revised Sequence

Chapter 3 - The Derivative

3.1 Tangents, Velocities, and Other Rates of Change 3.2 Derivatives 3.3 Rules for Differentiation 3.4 Product and Quotient Rules 3.5 Trigonometric Functions and Their Derivatives 3.6 Chain Rule 3.7 Parametric and Polar Differentiation 3.8 Implicit Differentiation 3.9 Inverse Functions and Their Derivatives 3.10 Logarithmic Functions and Their Derivatives

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Resequencing Calculus: Dwyer and Gruenwald Table of Contents

Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16

Revised Sequence

Chapter 4 - Applications of the Derivative

4.1 Maximum and Minimum Values 4.2 The Mean Value Theorem 4.3 Derivatives and Graphs 4.4 Optimization 4.5 Applications to Rates of Change 4.6 Indeterminate Limits and L’Hopital’s Rule 4.7 Polynomial Approximations 4.8 Tangent Line Approximations: Differentials and Newton’s Method

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Resequencing Calculus: Dwyer and Gruenwald Table of Contents

Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16

Revised Sequence

Chapter 5 - The Integral

5.1 Antiderivatives and Indefinite Integrals 5.2 Area Under a Curve and Total Change 5.3 The Definite Integral 5.4 The Fundamental Theorem of Calculus 5.5 Integration By Substitution

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Resequencing Calculus: Dwyer and Gruenwald Table of Contents

Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16

Revised Sequence

Chapter 6 - Techniques of Integration

6.1 Advanced Substitution techniques 6.2 Integration by Parts 6.3 Integrating Rational Functions 6.4 Improper Integrals 6.5 Approximating Definite Integrals

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Resequencing Calculus: Dwyer and Gruenwald Table of Contents

Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16

Revised Sequence

Chapter 7 - Applications of Integration

7.1 Average Value and Area Between Curves 7.2 Arc Length 7.3 Volumes 7.4 Solids of Revolution 7.5 Work 7.6 Probability

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Resequencing Calculus: Dwyer and Gruenwald Table of Contents

Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16

Revised Sequence

Chapter 8 - Differential Equations

8.1 Introduction To Differential Equations 8.2 Symbolic Solutions To Differential Equations 8.3 Graphical and Numerical Solutions To Differential Equations 8.4 Exponential Growth and Decay 8.5 Logistic Models 8.6 Linear First Order Differential Equations 8.7 Difference Equations

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Resequencing Calculus: Dwyer and Gruenwald Table of Contents

Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16

Revised Sequence

Chapter 9 - Vectors and Matrices

9.1 Vectors 9.2 Dot Product 9.3 Matrices 9.4 Determinants and Inverse Matrices 9.5 Cross Product 9.6 Lines and Planes in Space

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Resequencing Calculus: Dwyer and Gruenwald Table of Contents

Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16

Revised Sequence

Chapter 10 - Functions of Several Variables

10.1 Introduction to Functions of Several Variables 10.2 Limits and Continuity 10.3 Partial Derivatives 10.4 Chain Rule 10.5 Directional Derivatives and Gradients 10.6 Tangent Planes and Linear Approximations 10.7 Extrema and the Second Partials Test 10.8 Lagrange Multipliers

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Resequencing Calculus: Dwyer and Gruenwald Table of Contents

Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16

Revised Sequence

Chapter 11 - Double Integrals

11.1 Double Integrals over Rectangles 11.2 Double Integrals over Regions 11.3 Double Integrals in Polar Coordinates 11.4 Applications of Double Integrals

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Resequencing Calculus: Dwyer and Gruenwald Table of Contents

Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16

Revised Sequence

Chapter 12 - Infinite Series

12.1 Sequences of Partial Sums 12.2 Series 12.3 Integral Test 12.4 Comparison Tests 12.5 Alternating Series 12.6 Ratio and Root Tests 12.7 Power Series 12.8 Power Series Representations of Functions 12.9 Taylor Series 12.10 Fourier Series

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Resequencing Calculus: Dwyer and Gruenwald Table of Contents

Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16

Revised Sequence

Chapter 13 - Vector-Valued Functions

13.1 Review of Vectors 13.2 Vector-Valued Functions 13.3 Differentiation and Integration of Vector-Valued Functions 13.4 Arc Length and Curvature 13.5 Motion in Space 13.6 Tangent and Normal Vectors

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Resequencing Calculus: Dwyer and Gruenwald Table of Contents

Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16

Revised Sequence

Chapter 14 - Surfaces, Solids, and Multiple Integrals

14.1 Conic Sections 14.2 Cylinders and Quadric Surfaces 14.3 Review of Double Integrals 14.4 Surface Area 14.5 Integrals over Solids: Triple Integration 14.6 Cylindrical and Spherical Coordinates 14.7 Triple Integrals in Cylindrical and Spherical Coordinates 14.8 Change of Variables: The Jacobian

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Resequencing Calculus: Dwyer and Gruenwald Table of Contents

Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16

Revised Sequence

Chapter 15 - Vector Analysis

15.1 Vector Fields 15.2 Line Integrals 15.3 Conservative Vector Fields 15.4 Green’s Theorem 15.5 Parametric Surfaces 15.6 Surface Integrals 15.7 Divergence Theorem 15.8 Stoke’s Theorem

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Resequencing Calculus: Dwyer and Gruenwald Table of Contents

Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16

Revised Sequence

Chapter 16 - Differential Equations Revisited

16.1 Exact Differential Equations 16.2 Second-Order Linear Equations: Real Roots 16.3 Second-Order Linear Equations: Complex Roots 16.4 Series Solutions of Differential Equations 16.5 Systems of First-Order Equations

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Resequencing Calculus: Dwyer and Gruenwald Table of Contents

Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16

Revised Sequence

Revised Sequence

Course Section Count Typical Majors Calculus I 34 Math, Phys, Engr, Chem, Bio, Econ Calculus II 33 Math, Phys, Engr, Chem, Bio, Econ Calculus III 28 Math, Phys, Engr, Chem (Prof.)